How can I integrate my giveaway with GetResponse?

From your giveaway's setup page, click on the 'add another option' button:

From the list of options, click on the 'subscribing to a mailing list' button:

Click on the 'select your email provider' button:

Choose 'GetResponse' from the list:

Enter your API credentials, and click the 'validate credentials' button. You can locate these credentials by logging onto your paid account at http://www.getresponse.com/ then clicking 'Account Details' from the 'My Account' dropdown Menu in the header.

From there, click on 'GetResponse API' and copy the 'Secret API Key' on the screen.

Back in Rafflecopter, select your email list from the drop-down, fill out the rest of the form, and click the "save this option" button.